On the Adaptive Control of the False Discovery Rate in Multiple Testing With Independent Statistics

TLDR

Benjamini and Hochberg (1995) introduced controlling the False Discovery Rate (FDR) in multiple testing, but the method is overly conservative when many hypotheses are false. The authors propose an adaptive FDR procedure that estimates the number of true nulls before applying the Benjamini–Hochberg stepwise rule. The adaptive method remains a simple stepwise rule, illustrated with a graphical companion, and is applied to educational and behavioral examples covering multi‑center studies, subset analysis, and meta‑analysis, varying in hypothesis counts to show its impact. Simulations confirm that the adaptive procedure controls the FDR for independent tests and achieves substantially higher power than earlier FDR methods and traditional family‑wise error‑rate controls, with negligible penalty when most hypotheses are false.

Abstract

A new approach to problems of multiple significance testing was presented in Benjamini and Hochberg (1995), which calls for controlling the expected ratio of the number of erroneous rejections to the number of rejections–the False Discovery Rate (FDR). The procedure given there was shown to control the FDR for independent test statistics. When some of the hypotheses are in fact false, that procedure is too conservative. We present here an adaptive procedure, where the number of true null hypotheses is estimated first as in Hochberg and Benjamini (1990), and this estimate is used in the procedure of Benjamini and Hochberg (1995). The result is still a simple stepwise procedure, to which we also give a graphical companion. The new procedure is used in several examples drawn from educational and behavioral studies, addressing problems in multi-center studies, subset analysis and meta-analysis. The examples vary in the number of hypotheses tested, and the implication of the new procedure on the conclusions. In a large simulation study of independent test statistics the adaptive procedure is shown to control the FDR and have substantially better power than the previously suggested FDR controlling method, which by itself is more powerful than the traditional family wise error-rate controlling methods. In cases where most of the tested hypotheses are far from being true there is hardly any penalty due to the simultaneous testing of many hypotheses.